The Psychology of X-Men (2000)

Magneto and Professor X
Professor Charles Xavier and Erik Lehnsherr / Magneto are both older mutant leaders fighting for mutant rights, in two vastly differently ways. X-Men movies and comics have been related to the Civil Rights Movement, for obvious reasons, and Professor X is the Martin Luther King, Jr. to Magneto’s Malcolm X.
The issue with that being, Malcolm X wasn’t actually a villain. He just wasn’t a “good” civil rights leader because he advocated defense against police brutality whereas King preached passivism. Of course, at the time, neither civil rights leader was liked very much by the overall white population, and both were assassinated, but since then King has been romanticized and Malcolm X demonized.
So you have Prof. X the hero, and Magneto the villain. Charles introduces Magneto to Logan, saying "Believing that humanity would never accept us, he grew angry and vengeful. He became Magneto." Ok, but like, in 1944, child Erik was in a concentration camp and saw his parents carried off to the incinerator for being Jewish. Personally, if my parents were killed by Nazis, I would also have a visceral reaction to lawmakers wanting to register people who are different. Presumably Charles never faced such a trauma before. Magneto carries what happened in Nazi Poland to current times.
Still, Charles encourages Erik to hope that humanity learned from its mistakes all those decades ago and will behave different this time: “It was a long time ago. Mankind has evolved since then.” In one conversation, Erik appeals back to the Holocaust, "Let them pass that law. They'll have you in chains with a number burned into your forehead" [like the tattoo of the concentration camp number on his arm]. But Charles still, rather naively, hopes, "It won't be that way."

Erik does not have any such hope. He justifies his murderous actions, saying, "Women and children, whole families destroyed simply because they were born different from those in power." And to be fair, these atrocities did not stop after the Holocaust. People are still discriminated, hurt, and killed for being different, rather fictional mutants or real life groups.
Ok, so maybe at this point it’s obvious, but Magneto is one of my favorite “villains.” Many of his actions are awful. Kidnapping Rogue and using a child to protect himself is truly villainous. But I relate to his pessimism that majority groups in power have necessarily learned from history and evolved into more compassionate beings.
Rogue

The first time I watched this movie, (I was nine) I thought Rogue was such a cool character. Sarcastic, scrappy,
fashionable. Sixteen years later, my initial impression concerning Rogue is, who are these parents that let their teen daughter have her boyfriend in her room? That seems the most doubtful part of this movie.
But I digress.
Rogue is probably the most outcast of the outcasts. Not only is she different from society, her ability isolates her from physical human contact. While she has always planned to travel, Rogue runs away from home at this point mostly to protect the people she cares about. Once she leaves, she finds prejudice and discrimination against other mutants, more reason to not draw attention to herself. Non-mutant humans fear and hate mutants, and if they knew Rogue’s power, she would be even more targeted. She is alone and in hiding.
Until she finds Logan. She discovers he’s a mutant like herself when he uses his claws in a bar fight. The man literally attacks a man and cuts a shot gun in half, and Rogue immediately follows. Rogue takes out after this guy who's dangerous as hell. Why isn't she scared of him? Perhaps at this point Rogue has been isolated for so long that once she sees someone who is like her, she ignores the danger. She readily assumes that since she is also like him, he will accept her.
Fortunately, Rogue finds a place for herself at Xavier’s school. Despite her mutant status and isolating ability, Charles observes, "Yet here she is with others her own age, learning, being accepted, not feared." Away from mainstream society, Rogue finds friends, mentors, and parental figures who accept her. She no longer has to hide.
Senator Kelly
Almost every X-Men movie has a main character who leads the anti-mutant movement, and in this film Senator Kelly does the job. He wants to pass a law forcing to all mutants to identify themselves and their powers. Jean Grey tries to convince anti-mutant pro-registration legislators the dangers of this through conversation and diplomacy. Kelly, however, appeals to their fears and is held up as a hero.
He privately confesses, "If it were up to me, I'd lock them all away. It's a war. It's the reason why people like me exist." Not only do the people view Kelly as a sort of savior from the mutants, he views himself this way. His mission in life isn’t just to earn votes like any politician, but to continue the us versus them dynamic society as created.
But Kelly is kidnapped by the Brotherhood of Mutants and is forced to hear a much-needed lecture on social dynamics. Magneto tells the senator, "Mankind has always feared what it doesn't understand."
Kelly fears and, therefore, hates the mutants because he does not understand them. So, Magneto solves this problem by making the senator into a mutant. Which, I mean, this maybe isn’t the best plan, but it isn't necessarily illogical.

Psychologist Muzafer Sherif conducted an experiment (Robbers Cave Experiment) in which two groups of adolescent boys were pitted against each other in competition. Sherif’s goal was to create intergroup conflict through competitive team games between the two groups. According to Sherif’s Realistic Conflict Theory, hatred between groups of people arises when those groups must compete for resources, or in the experiment, for really cool prizes.
These boys had no real reason to start coming up with stereotypes and prejudices about each other, except that they were separated and working against each other. After the boys officially grew to dislike each other just based on their groups, Sherif wanted to reverse the feelings. In order to do this, he had the groups work together to solve a problem.
By working together, the boys stopped thinking of themselves and each other in terms of “us versus them.” They merged into one group and started to identify with each other. Which, in his own demented way, Magneto tries to merge the humans, starting with Senator Kelly, and the mutants into one group by turning the world leaders into mutants. As a mutant, Senator Kelly would no longer be able to think of mutants as “them” but rather us “us.”
The senator goes to the mansion looking for Jean Grey. Charles tries to help the senator understand that not all mutants are dangerous, but Kelly replies, oozing internalized mutant hate, "Tell it to the ones who did this to me."
However, despite these feelings, the senator seeks comfort from Storm as he lays dying. He asks her, "Do you hate normal people? …Why?" Why? Senator, in all fairness, you admitted to wanting to lock all mutants up earlier in the film. His last words are, "Well, I think you got one less person to be afraid of." This statement can be taken a couple of ways. Either he knows he's about to die, or he's changed his position on mutants. Perhaps, and this is a fairly optimistic perhaps, he’s telling Storm that she no longer needs to fear him because he no longer wants to hurt her.
Wolverine

Logan appears hyper-vigilant, aggressive, and defensive when he first arrives at the mansion and throughout the movie. His first night at the mansion he has nightmares or flashbacks of the experiment that implanted adamantium onto his skeleton. This behavior and symptoms points directly at post-traumatic stress disorder. In addition to a possible PTSD diagnosis, Logan has no memory of his past before the experimental surgery, just since. Jean Grey, however, can telepathically unlock those memories. Essentially Logan’s memories are still in his mind; he is just unable to retrieve to retrieve them.
For an actual diagnosis, I went through the APA’s Diagnostic Statistical Manual – 5 criteria for PTSD.
Criterion A (one required): The person was exposed to: death, threatened death, actual or threatened serious injury, or actual or threatened sexual violence, in the following way(s):
Direct exposure – Yes, he could have theoretically died during the experiment.
Witnessing the trauma
Learning that a relative or close friend was exposed to a trauma
Indirect exposure to aversive details of the trauma, usually in the course of professional duties (e.g., first responders, medics)
Criterion B (one required): The traumatic event is persistently re-experienced, in the following way(s):
Intrusive thoughts
Nightmares – Yes
Flashbacks
Emotional distress after exposure to traumatic reminders
Physical reactivity after exposure to traumatic reminders
Criterion C (one required): Avoidance of trauma-related stimuli after the trauma, in the following way(s):
Trauma-related thoughts or feelings
Trauma-related reminders – Perhaps? He does actively go searching for reminders of the trauma, in order to piece together his past, but when first meeting Prof. X, he tells him to shut up about it.
Criterion D (two required): Negative thoughts or feelings that began or worsened after the trauma, in the following way(s):
Inability to recall key features of the trauma – Yes
Overly negative thoughts and assumptions about oneself or the world – Yes, or at least appears to.
Exaggerated blame of self or others for causing the trauma – Doesn’t appear so.
Negative affect – Yes
Decreased interest in activities – Unsure
Feeling isolated – Yes, but most mutants do, so this may be unrelated to the trauma.
Difficulty experiencing positive affect – Logan does not appear particularly happy during the film, but that could be circumstantial, considering he thinks Magneto is hunting him.
Criterion E (two required): Trauma-related arousal and reactivity that began or worsened after the trauma, in the following way(s): Firstly, comparing his past behavior with his current behavior is impossible at this point with information from the movie since he does not remember.
Irritability or aggression – Yes
Risky or destructive behavior – Yes
Hypervigilance – Yes
Heightened startle reaction – Yes
Difficulty concentrating – Not apparent
Difficulty sleeping – Yes
Criterion F (required): Symptoms last for more than 1 month. – presumably so.
Criterion G (required): Symptoms create distress or functional impairment (e.g., social, occupational). – Logan is isolated and doesn’t have social relationships presumably until coming to the mansion. Even then, he has difficulty creating bonds, except with Rogue.
Criterion H (required): Symptoms are not due to medication, substance use, or other illness. Unknown for sure.
Two specifications:
Dissociative Specification. In addition to meeting criteria for diagnosis, an individual experiences high levels of either of the following in reaction to trauma-related stimuli:
Depersonalization. experience of being an outside observer of or detached from oneself (e.g., feeling as if "this is not happening to me" or one were in a dream).
Derealization: experience of unreality, distance, or distortion (e.g., "things are not real").
Delayed Specification. Full diagnostic criteria are not met until at least six months after the trauma(s), although onset of symptoms may occur immediately.
Logan does not appear to meet any of these specifications. He does, however, have some form of retrograde amnesia, being able to create new memories but not access old memories, in addition to meeting criteria for PTSD. At this point, it is impossible to access whether this amnesia is caused by the trauma, the PTSD, or some other cause.